Error detection coding can be used to detect errors in decoding information that has been encoded using a code.
Polar codes, for example, are proposed as channel codes for use in future wireless communications, and have been selected for uplink and downlink eMBB control channel coding for the new 5th Generation (5G) air interface, also known as the 5G New Radio (NR). These codes are competitive with state-of-the-art error correction codes and have low encoding complexity. See E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 3051-3073, 2009. Successive Cancellation (SC) decoding and its extension SC List (SCL) decoding, are effective and efficient options for decoding polar coded information.
Based on channel polarization, Arikan designed a channel code that is proven to achieve the capacity of symmetric channels. Polarization refers to a coding property that, as code length increases to infinity, bit-channels also referred to as sub-channels polarize and their capacities approach either zero (completely noisy channel) or one (completely perfect channel). In other words, bits encoded in high capacity sub-channels will experience a synthesized channel with equivalently high Signal-to-Noise Ratio (SNR), and will have a relatively high reliability or a high likelihood of being correctly decoded, and bits encoded in low capacity sub-channels will have low reliability or a low possibility to be correctly decoded. The fraction of perfect bit-channels is equal to the capacity of a channel.